Initially, this problem was mentioned in the context of acoustics in [1]} (1945). Much later (2004), the interest to this problem was renewed due to relation to molecular biology and biophysics; see [2]}. Many problems in cellular biology may be formulated as mean sojourn time problems; a collection of analysis methods, results, applications, and references may be found in [3]} and [4]}. For example, cells have been modelled as simply connected two-dimensional domains with small absorbing windows on the boundary representing ion channels or target binding sites; the quantity sought is then the mean time for a diffusing ion or receptor to exit through an ion channel or reach a binding site [5]}, [2]}, [7]}. All of this lead to the narrow escape theory in applied mathematics and computational biology; see [8]}, [9]}, [10]}.
